Numerical analysis of grasshopper escapement
David Ziemkiewicz
TL;DR
This paper numerically investigates the dynamics of driven, damped pendulums in mechanical clocks, focusing on Harrison's grasshopper escapement, revealing insights into its stability, transient behaviors, and potential for chaotic motion.
Contribution
It provides a detailed numerical analysis of the grasshopper escapement, highlighting its unique properties and conditions for stable long-term operation.
Findings
Insights into stable operation conditions
Analysis of transient effects
Investigation of chaotic motion potential
Abstract
The dynamics of driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of a well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper escapement are explored, giving some insights regarding the dynamics of this system. Both steady state operation and transient effects are discussed, indicating the optimal condition for stable long-term clock accuracy. Possibility of chaotic motion is investigated.
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